CN108595765B - Wind generating set double-row tapered roller bearing load distribution and service life calculation method - Google Patents

Wind generating set double-row tapered roller bearing load distribution and service life calculation method Download PDF

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CN108595765B
CN108595765B CN201810255895.1A CN201810255895A CN108595765B CN 108595765 B CN108595765 B CN 108595765B CN 201810255895 A CN201810255895 A CN 201810255895A CN 108595765 B CN108595765 B CN 108595765B
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roller
coordinate system
inner ring
raceway
bearing
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CN108595765A (en
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邹荔兵
段博志
杨明川
黄翀
任永
赵春雨
刘凡鹰
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MingYang Smart Energy Group Co Ltd
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Abstract

The invention discloses a load distribution and service life calculation method for a double-row tapered roller bearing of a wind generating set, which mainly simulates the deformation of an inner ring and a rolling body of the double-row tapered roller bearing based on coordinate vectors, particularly reflects the contact deformation of a raceway and a roller and the contact deformation of the roller and a flange through coordinate transformation, considers the influences of flange deformation, bearing play and roller modification, obtains the load distribution of the bearing raceway by establishing a static equilibrium equation of the raceway and the roller, and then solves the service life of the bearing on the basis. The method can efficiently, accurately and quickly calculate the load distribution and the service life of the bearing, and has practical popularization value.

Description

Wind generating set double-row tapered roller bearing load distribution and service life calculation method
Technical Field
The invention relates to the technical field of component strength analysis of wind generating sets, in particular to a load distribution and service life calculation method for a double-row tapered roller bearing of a wind generating set.
Background
The double-row tapered roller bearing is an important part of a transmission system of a large-scale wind generating set, and is widely applied to main shaft bearings of semi-direct-drive fans and direct-drive fans. The bearing load working condition is complex and changeable, the stress condition inside the bearing is complex in the operation process, and the load distribution calculation is difficult.
In view of the above, a method for simulating deformation of a double-row conical bearing inner ring and a roller based on coordinate vectors is provided, the contact deformation of a raceway and the roller is reflected through coordinate conversion, the influence of a flange model, a bearing clearance and the like is considered in the model, and the load distribution of the bearing raceway can be more accurately solved.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method for calculating load distribution and service life of a double-row tapered roller bearing of a wind generating set, and can efficiently, accurately and quickly calculate the load distribution and the service life of the bearing.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a load distribution and service life calculation method for a double-row tapered roller bearing of a wind generating set is mainly characterized in that deformation of an inner ring and a rolling body of the double-row tapered roller bearing is simulated based on coordinate vectors, specifically, contact deformation of a raceway and a roller and contact deformation of the roller and a flange are reflected through coordinate transformation, influences of flange deformation, bearing play and roller modification are considered, load distribution of the bearing raceway is obtained by establishing a hydrostatic equilibrium equation of the raceway and the roller, and then the service life of the bearing is solved on the basis; which comprises the following steps:
1) simulating the position vectors of the rollers and the roller paths and the rollers and the flanges of the bearing before and after deformation through coordinate vectors, and then converting the vector coordinates of the contact point from a roller coordinate system and an inner ring coordinate system to a system coordinate system through coordinate conversion to establish a deformation coordination equation;
2) establishing a roller static equilibrium equation and a bearing outer ring static equilibrium equation according to a deformation coordination equation, and performing iterative solution on accurate load distribution of a raceway and a flange according to a Newton-Raphson equation;
3) the basic rated service life and the corrected service life of the double-row tapered roller bearing are solved according to the load distribution of the bearing raceway, the bearing raceway is sliced by adopting a slicing method in the solving process, the service life of each slice is respectively solved, and then the service life of the whole bearing is obtained through integration.
The step 1) comprises the following specific steps:
1.1) establishing a system coordinate system Oxyz by taking the center of the bearing as an origin, and establishing an inner ring coordinate system O by taking the center of the inner ring as the originhxhyhzhEstablishing a roller coordinate system O with the roller center as the originwh xwh ywh zwhH represents the column;
1.2) determining the amount of deformation
1.2.1) inner ring deformation
Under the coordinate system of the inner ring, the displacement vector of the inner ring under the action of an external load is as follows:
δh＝{δhx,δhy,δhz}T (1)
the vector of the deflection angle of the inner ring is as follows:
γh＝{0,γhy,γhz}T (2)
the coordinates of the center of the inner ring in 3 directions after considering the bearing play are as follows:
Figure GDA0003292529820000021
Figure GDA0003292529820000022
Figure GDA0003292529820000023
in the formula: deltahx，δhy，δhzRespectively, the displacement of the center of the inner ring coordinate system when the play is not considered; gamma rayhy,γhzRespectively as the center of the inner ringh，zhThe angle of deflection of the shaft; delta 'of'hx，δ′hy，δ′hzThe displacement of the center of the inner ring coordinate system when the radial play is considered; e.g. of the typerThe distance from the center of the inner ring coordinate system to the center of the system coordinate system; grIs a radial play; when h is equal to 1, the reaction is carried out,
Figure GDA0003292529820000031
when h is 2, taking the positive value and taking the negative value as the positive value,
Figure GDA0003292529820000032
taking-;
1.2.2) roller deformation
In the roller coordinate system, the displacement vector of the roller is as follows:
Uwh＝{uwhx,0,uwhz}T (6)
the roller rotation angle vector is:
Figure GDA0003292529820000033
in the formula: u. ofwhx，uwhzRespectively, the roller is at xwh，zwhDisplacement of direction;
Figure GDA0003292529820000034
for rolling of rollerswhThe angle of rotation of the direction;
1.3) determining the position of the contact point before deformation
1.3.1) inner circle coordinate System
Z is the contact point of the inner and outer ring raceways and the rollers under the roller coordinate systemwhThe coordinates in the axial direction are:
Figure GDA0003292529820000035
Figure GDA0003292529820000036
Figure GDA0003292529820000037
Figure GDA0003292529820000038
in the formula: dpwThe diameter of the pitch circle of the roller group; x is the number ofwhi，xwheX is the contact point of the inner raceway and the outer raceway of the ferrule and the roller respectively under the roller coordinate systemwhCoordinates of the axis; epsilon is the roller half-cone angle; alpha and beta are respectively half cone angles of an outer raceway and an inner raceway; γ is the bearing contact angle, c is the normal clearance, when h is 1, c is-1, when h is 2, c is 1; l is the roller length;
the position vectors of the contact points of the inner raceway, the outer raceway and the roller under the inner ring coordinate system are as follows:
Figure GDA0003292529820000041
Figure GDA0003292529820000042
in the formula: e is the axial distance between the center of the roller coordinate system and the center of the inner ring coordinate system; r ishix,rhiy,rhizThe coordinates of the contact point of the roller and the inner raceway under an inner ring coordinate system; r ishex,rhey,rhezThe coordinates of the contact point of the roller and the outer raceway in 3 directions under an inner ring coordinate system are obtained; psi is the azimuth angle of the roller, the roller corresponding to the negative direction of the z-axis in the system coordinate system is the 1 st roller, the azimuth angle is 0, and the azimuth angle of the jth roller is
Figure GDA0003292529820000043
Z is the number of single-row rollers;
the end part of the roller adopts a spherical base surface, and the position vector of the contact point of the roller and the flange under the inner ring coordinate system is as follows:
Figure GDA0003292529820000044
Figure GDA0003292529820000045
in the formula: r ishfx,rhfy,rhfzThe coordinates of the contact point of the roller and the flange in 3 directions under the inner ring coordinate system are obtained; rsIs the radius of the spherical base surface; theta is an included angle between a connecting line of the inner ring flange and the center of the bearing and the x direction; dwThe diameter of the large end of the roller is adopted, and lambda is a half angle corresponding to the base surface of the ball of the roller;
1.3.2) roller coordinate System
The position vector of the contact point of the roller and the inner and outer raceways under the roller coordinate system is as follows:
Figure GDA0003292529820000051
Figure GDA0003292529820000052
the position vector of the contact point of the roller and the flange under the roller coordinate system is as follows:
Figure GDA0003292529820000053
in the formula: swhfx，swhfy，swhfzCoordinates of the contact point of the roller and the flange in 3 directions under a roller coordinate system are obtained;
1.4) determining the position of the contact point after deformation
1.4.1) inner circle coordinate System
After the inner ring is deformed in a contact manner, the position vector of the contact point of the inner ring raceway and the roller under the inner ring coordinate system is as follows:
Figure GDA0003292529820000054
in the formula:
Figure GDA0003292529820000055
coordinates of the contact point of the inner ring raceway and the roller in 3 directions under an inner ring coordinate system; when h is equal to 1, the reaction is carried out,
Figure GDA0003292529820000056
when h is 2, taking the positive value and taking the negative value as the positive value,
Figure GDA0003292529820000057
taking-;
because the outer raceway is fixed, the position vector of the contact point of the outer raceway and the roller on the inner ring coordinate system is consistent with that before deformation, namely
Figure GDA0003292529820000058
The position vector of the contact point of the roller and the flange under the inner ring coordinate system is as follows:
Figure GDA0003292529820000061
in the formula:
Figure GDA0003292529820000062
the coordinates of the position vector of the contact point of the roller and the flange in 3 directions under the inner ring coordinate system are obtained;
1.4.2) roller coordinate System
The position vector of the contact point of the roller and the inner and outer raceways under the roller coordinate system after the roller is deformed is as follows:
Figure GDA0003292529820000063
Figure GDA0003292529820000064
the position vector of the contact point of the roller and the flange under the roller coordinate system is as follows:
Figure GDA0003292529820000065
1.5) deformation coordination equation
Converting the contact point from the roller coordinate system and the inner ring coordinate system to the system coordinate system through coordinate conversion, then
Figure GDA0003292529820000066
Figure GDA0003292529820000067
Figure GDA0003292529820000068
Figure GDA0003292529820000071
ew＝e+er
Figure GDA0003292529820000072
In the formula: e.g. of the typewIs the distance from the center of the roller coordinate system to the center of the system coordinate system, when h is 1
Figure GDA0003292529820000073
Taken + and taken when h is 2
Figure GDA0003292529820000074
Taking-;
the normal contact deformation of the roller, the inner raceway, the outer raceway and the flange is as follows:
Figure GDA0003292529820000075
Figure GDA0003292529820000076
Figure GDA0003292529820000077
Figure GDA0003292529820000078
Figure GDA0003292529820000079
Figure GDA00032925298200000710
in the formula:
Figure GDA00032925298200000711
respectively are unit normal vectors of the inner ring, the outer ring and the flange; when h is 1
Figure GDA00032925298200000712
Taken + and taken when h is 2
Figure GDA00032925298200000713
Take the value of.
In step 2), the details of the roller static balance equation are as follows:
and (3) carrying out stress analysis on a single roller, wherein the balance equation is as follows:
Qi+Qe+Fc＝0 (28)
Ti+Te+Mg＝0 (29)
Figure GDA00032925298200000714
Figure GDA0003292529820000081
Figure GDA0003292529820000082
Figure GDA0003292529820000083
Figure GDA0003292529820000084
Mg＝JrωGωZsinγ (35)
in the formula: ki,KeThe contact stiffness of the inner ring and the outer ring is respectively; qi，QeRespectively the contact part load of the roller and the inner ring and the contact part load of the outer ring; t isi，TeThe moment acted on the roller by the inner and outer ring raceways respectively; fcIs the centrifugal force of the roller; mgA gyroscopic moment that is a roller; m is the mass of a single tapered roller; rGThe radius of rotation of the roller centroid; omegaGIs the revolution angular velocity of the roller; j. the design is a squarerIs the roller moment of inertia; omegaZIs the roller rotation angular velocity; deltahi(xwhiψ) is the normal contact deformation of the roller with the inner raceway, δhe(xwhePsi) is the normal contact deformation of the roller and the outer raceway; x is the number ofwhi，xwheX is the contact point of the inner raceway and the outer raceway of the ferrule and the roller respectively under the roller coordinate systemwhCoordinates of the axis; psi is the roller azimuth; gamma is the contact angle of the bearing;
the outer ring static equilibrium equation has the following specific conditions:
and (3) carrying out stress analysis on the outer ring, wherein the balance equation is as follows:
Figure GDA0003292529820000085
Figure GDA0003292529820000086
Figure GDA0003292529820000087
Figure GDA0003292529820000088
Figure GDA0003292529820000089
Figure GDA0003292529820000091
Figure GDA0003292529820000092
in the formula: fx，Fy，Fz，My，MzThe loads in five directions at the center of the bearing; q. q.sheThe contact load is the contact load of the outer ring and the roller contact point position in unit length; when h is 1
Figure GDA0003292529820000093
Taken + and taken when h is 2
Figure GDA0003292529820000094
Taking-;
the statics equilibrium equation solving process is as follows:
solving according to the established roller static balance equation and the outer ring static balance equation, wherein the solving process comprises the following steps: 1) inputting main structural parameters of a bearing: l, Rs，Dw，θ，α，β，Z，e，er，Gr(ii) a 2) Inputting working condition parameters: fx，Fy，Fz，My，Mz(ii) a 3) Giving a roller deformation initial value and an inner ring deformation initial value; 4) performing iterative calculation through formulas (28) to (42) to obtain raceway load distribution;
wherein l is the roller length; rsIs the radius of the spherical base surface; dwThe diameter of the big end of the roller; theta is an included angle between a connecting line of the inner ring flange and the center of the bearing and the x direction; alpha and beta are respectively half cone angles of an outer raceway and an inner raceway; z isThe number of single row rollers; e is the axial distance between the center of the roller coordinate system and the center of the inner ring coordinate system; e.g. of the typerThe distance from the center of the inner ring coordinate system to the center of the system coordinate system; grIs a radial play.
In the step 3), the bearing load distribution condition is obtained according to the statics equilibrium equation, and then the service life of the raceway can be solved, specifically as follows:
dividing a bearing raceway into n equal parts, wherein the service life of each section is as follows:
Figure GDA0003292529820000095
Figure GDA0003292529820000096
in the formula: qCihtThe basic rated load of the roller way in the t slice; qCehtThe basic rated load of the roller way in the t slice; qEihtThe equivalent load of the inner raceway of the t-th slice; qEehtThe equivalent load of the t slice outer raceway is shown;
the basic nominal load of each slice is:
Figure GDA0003292529820000101
Figure GDA0003292529820000102
in the formula: bmA rated life correction factor; lambda [ alpha ]sCorrection coefficients introduced to correct edge loading and stress concentrations of the roller; Δ l is the length of each slice; dtRoll diameter for the t slice; dpwThe diameter of the pitch circle of the roller group; gamma is a bearing contact angle; gamma ray*Is the structural coefficient of the bearing;
the equivalent load per section of the raceway of the inner ring, i.e. the rotating ring, is:
Figure GDA0003292529820000103
the equivalent load per section of the raceway of the outer ring, i.e. the stationary ferrule, is:
Figure GDA0003292529820000104
the service life of the inner ring and the outer ring of the single-row bearing is as follows:
Figure GDA0003292529820000105
Figure GDA0003292529820000106
the comprehensive service life of the inner ring and the outer ring of the single-row bearing is as follows:
L10m＝L10im+L10em (50)
the basic rated life of the whole bearing is as follows:
Figure GDA0003292529820000107
the whole bearing correction service life is as follows:
La10DRTRB＝a1aisoL10DRTRB (52)
in the above formula: psi is the roller azimuth angle, qihThe contact load is the unit length of the inner ring; q. q.sehThe contact load is the unit length of the outer ring; a is1Is a reliability coefficient; a isisoIs the lube oil coefficient.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the problems of flange deformation, bearing radial play, roller modification and the like are not considered in the calculation of the transmission double-row tapered roller bearing, and the influence of the flange deformation, the bearing play and the roller modification on the load distribution of the bearing raceway is considered in the method, so that more accurate raceway load distribution is obtained.
2. The method reflects the contact deformation of the raceway and the roller through coordinate transformation, and the contact deformation of the roller and the flange can be analyzed more accurately.
3. The method slices the bearing, and can more truly simulate the load distribution of the roller along the length direction of the roller through shearing.
Drawings
FIG. 1 is a schematic structural view of a double-row tapered roller bearing according to the present invention.
FIG. 2 is a schematic view of the rollers of the present invention in contact with the ribs.
Detailed Description
The present invention will be further described with reference to the following specific examples.
The load distribution and service life calculation method for the double-row tapered roller bearing of the wind generating set, provided by the embodiment, aims at the problems that flange deformation, bearing radial play, roller modification and the like are not considered in an internal load calculation model of a traditional double-row tapered roller bearing, and provides a method for simulating deformation of an inner ring and a rolling element of the double-row tapered roller bearing based on a coordinate vector, particularly reflects contact deformation of a raceway and a roller and contact deformation of the roller and the flange through coordinate transformation, considers the influences of flange deformation, bearing play and roller modification, obtains load distribution of the bearing raceway by establishing a hydrostatic equilibrium equation of the raceway and the roller, and then solves the service life of the bearing on the basis; the specific situation is as follows:
1) simulating the position vectors of the rollers and the roller paths and the rollers and the flanges of the bearing before and after deformation through coordinate vectors, and then converting the vector coordinates of the contact point from a roller coordinate system and an inner ring coordinate system to a system coordinate system through coordinate conversion to establish a deformation coordination equation; the method specifically comprises the following steps:
1.1) double-row tapered roller bearing structure for wind driven generator As shown in FIG. 1, a system coordinate system Oxyz is established with the center of the bearing as the origin, and an inner ring seat is established with the center of the inner ring as the originSystem of symbols OhxhyhzhEstablishing a roller coordinate system O with the roller center as the originwh xwh ywh zwhH represents the column;
1.2) determining the amount of deformation
1.2.1) inner ring deformation
Under the coordinate system of the inner ring, the displacement vector of the inner ring under the action of an external load is as follows:
δh＝{δhx,δhy,δhz}T (1)
the vector of the deflection angle of the inner ring is as follows:
γh＝{0,γhy,γhz}T (2)
the coordinates of the center of the inner ring in 3 directions after considering the bearing play are as follows:
Figure GDA0003292529820000121
Figure GDA0003292529820000122
Figure GDA0003292529820000123
in the formula: deltahx，δhy，δhzRespectively, the displacement of the center of the inner ring coordinate system when the play is not considered; gamma rayhy,γhzRespectively as the center of the inner ringh，zhThe angle of deflection of the shaft; delta 'of'hx，δ′hy，δ′hzThe displacement of the center of the inner ring coordinate system when the radial play is considered; e.g. of the typerThe distance from the center of the inner ring coordinate system to the center of the system coordinate system; grIs a radial play; when h is equal to 1, the reaction is carried out,
Figure GDA0003292529820000124
when h is 2, taking the positive value and taking the negative value as the positive value,
Figure GDA0003292529820000125
taking-;
1.2.2) roller deformation
In the roller coordinate system, the displacement vector of the roller is as follows:
Uwh＝{uwhx,0,uwhz}T (6)
the roller rotation angle vector is:
Figure GDA0003292529820000131
in the formula: u. ofwhx，uwhzRespectively, the roller is at xwh，zwhDisplacement of direction;
Figure GDA0003292529820000132
for rolling of rollerswhThe angle of rotation of the direction;
1.3) determining the position of the contact point before deformation
1.3.1) inner circle coordinate System
Z is the contact point of the inner and outer ring raceways and the rollers under the roller coordinate systemwhThe coordinates in the axial direction are:
Figure GDA0003292529820000133
Figure GDA0003292529820000134
Figure GDA0003292529820000135
Figure GDA0003292529820000136
in the formula: dpwThe diameter of the pitch circle of the roller group; x is the number ofwhi，xwheX is the contact point of the inner raceway and the outer raceway of the ferrule and the roller respectively under the roller coordinate systemwhCoordinates of the axis; epsilon is the roller half-cone angle; alpha and beta are respectively half cone angles of an outer raceway and an inner raceway; γ is the bearing contact angle, c is the normal clearance, when h is 1, c is-1, when h is 2, c is 1; l is the roller length;
the position vectors of the contact points of the inner raceway, the outer raceway and the roller under the inner ring coordinate system are as follows:
Figure GDA0003292529820000141
Figure GDA0003292529820000142
in the formula: e is the axial distance between the center of the roller coordinate system and the center of the inner ring coordinate system; r ishix,rhiy,rhizThe coordinates of the contact point of the roller and the inner raceway under an inner ring coordinate system; r ishex,rhey,rhezThe coordinates of the contact point of the roller and the outer raceway in 3 directions under an inner ring coordinate system are obtained; psi is the azimuth angle of the roller, the roller corresponding to the negative direction of the z-axis in the system coordinate system is the 1 st roller, the azimuth angle is 0, and the azimuth angle of the jth roller is
Figure GDA0003292529820000143
Z is the number of single-row rollers;
the schematic contact diagram of the roller and the rib is shown in fig. 2, the end of the roller adopts a spherical base surface, and the position vector of the contact point of the roller and the rib under an inner ring coordinate system is as follows:
Figure GDA0003292529820000144
Figure GDA0003292529820000145
in the formula: r ishfx,rhfy,rhfzThe coordinates of the contact point of the roller and the flange in 3 directions under the inner ring coordinate system are obtained; rsIs the radius of the spherical base surface; theta is an included angle between a connecting line of the inner ring flange and the center of the bearing and the x direction; dwThe diameter of the large end of the roller is adopted, and lambda is a half angle corresponding to the base surface of the ball of the roller;
1.3.2) roller coordinate System
The position vector of the contact point of the roller and the inner and outer raceways under the roller coordinate system is as follows:
Figure GDA0003292529820000151
Figure GDA0003292529820000152
the position vector of the contact point of the roller and the flange under the roller coordinate system is as follows:
Figure GDA0003292529820000153
in the formula: swhfx，swhfy，swhfzCoordinates of the contact point of the roller and the flange in 3 directions under a roller coordinate system are obtained;
1.4) determining the position of the contact point after deformation
1.4.1) inner circle coordinate System
After the inner ring is deformed in a contact manner, the position vector of the contact point of the inner ring raceway and the roller under the inner ring coordinate system is as follows:
Figure GDA0003292529820000154
in the formula:
Figure GDA0003292529820000155
coordinates of the contact point of the inner ring raceway and the roller in 3 directions under an inner ring coordinate system; when h is equal to 1, the reaction is carried out,
Figure GDA0003292529820000156
when h is 2, taking the positive value and taking the negative value as the positive value,
Figure GDA0003292529820000157
taking-;
because the outer raceway is fixed, the position vector of the contact point of the outer raceway and the roller on the inner ring coordinate system is consistent with that before deformation, namely
Figure GDA0003292529820000158
The position vector of the contact point of the roller and the flange under the inner ring coordinate system is as follows:
Figure GDA0003292529820000161
in the formula:
Figure GDA0003292529820000162
the coordinates of the position vector of the contact point of the roller and the flange in 3 directions under the inner ring coordinate system are obtained;
1.4.2) roller coordinate System
The position vector of the contact point of the roller and the inner and outer raceways under the roller coordinate system after the roller is deformed is as follows:
Figure GDA0003292529820000163
Figure GDA0003292529820000164
the position vector of the contact point of the roller and the flange under the roller coordinate system is as follows:
Figure GDA0003292529820000165
1.5) deformation coordination equation
Converting the contact point from the roller coordinate system and the inner ring coordinate system to the system coordinate system through coordinate conversion, then
Figure GDA0003292529820000166
Figure GDA0003292529820000167
Figure GDA0003292529820000168
Figure GDA0003292529820000169
ew＝e+er
Figure GDA0003292529820000171
In the formula: e.g. of the typewIs the distance from the center of the roller coordinate system to the center of the system coordinate system, when h is 1
Figure GDA0003292529820000172
Taken + and taken when h is 2
Figure GDA0003292529820000173
Taking-;
the normal contact deformation of the roller, the inner raceway, the outer raceway and the flange is as follows:
Figure GDA0003292529820000174
Figure GDA0003292529820000175
Figure GDA0003292529820000176
Figure GDA0003292529820000177
Figure GDA0003292529820000178
Figure GDA0003292529820000179
in the formula:
Figure GDA00032925298200001710
respectively are unit normal vectors of the inner ring, the outer ring and the flange; when h is 1
Figure GDA00032925298200001711
Taken + and taken when h is 2
Figure GDA00032925298200001712
Take the value of.
2) Establishing a roller static equilibrium equation and a bearing outer ring static equilibrium equation according to a deformation coordination equation, and performing iterative solution on accurate load distribution of a raceway and a flange according to a Newton-Raphson equation; the specific conditions of the roller static equilibrium equation are as follows:
and (3) carrying out stress analysis on a single roller, wherein the balance equation is as follows:
Qi+Qe+Fc＝0 (28)
Ti+Te+Mg＝0 (29)
Figure GDA0003292529820000181
Figure GDA0003292529820000182
Figure GDA0003292529820000183
Figure GDA0003292529820000184
Figure GDA0003292529820000185
Mg＝JrωGωZsinγ (35)
in the formula: ki,KeThe contact stiffness of the inner ring and the outer ring is respectively; qi，QeRespectively the contact part load of the roller and the inner ring and the contact part load of the outer ring; t isi，TeThe moment acted on the roller by the inner and outer ring raceways respectively; fcIs the centrifugal force of the roller; mgA gyroscopic moment that is a roller; m is the mass of a single tapered roller; rGThe radius of rotation of the roller centroid; omegaGIs the revolution angular velocity of the roller; j. the design is a squarerIs the roller moment of inertia; omegaZIs the roller rotation angular velocity; deltahi(xwhiψ) is the normal contact deformation of the roller with the inner raceway, δhe(xwhePsi) is the normal contact deformation of the roller and the outer raceway; x is the number ofwhi，xwheX is the contact point of the inner raceway and the outer raceway of the ferrule and the roller respectively under the roller coordinate systemwhCoordinates of the axis; psi is the roller azimuth; gamma is the contact angle of the bearing;
the outer ring static equilibrium equation has the following specific conditions:
and (3) carrying out stress analysis on the outer ring, wherein the balance equation is as follows:
Figure GDA0003292529820000186
Figure GDA0003292529820000187
Figure GDA0003292529820000188
Figure GDA0003292529820000189
Figure GDA0003292529820000191
Figure GDA0003292529820000192
Figure GDA0003292529820000193
in the formula: fx，Fy，Fz，My，MzThe loads in five directions at the center of the bearing; q. q.sheThe contact load is the contact load of the outer ring and the roller contact point position in unit length; when h is 1
Figure GDA0003292529820000194
Taken + and taken when h is 2
Figure GDA0003292529820000195
Taking-;
the statics equilibrium equation solving process is as follows:
solving according to the established roller static balance equation and the outer ring static balance equation, wherein the solving process comprises the following steps: 1) input bearing mainThe structural parameters are as follows: l, Rs，Dw，θ，α，β，Z，e，er，Gr(ii) a 2) Inputting working condition parameters: fx，Fy，Fz，My，Mz(ii) a 3) Giving a roller deformation initial value and an inner ring deformation initial value; 4) performing iterative calculation through formulas (28) to (42) to obtain raceway load distribution;
wherein l is the roller length; rsIs the radius of the spherical base surface; dwThe diameter of the big end of the roller; theta is an included angle between a connecting line of the inner ring flange and the center of the bearing and the x direction; alpha and beta are respectively half cone angles of an outer raceway and an inner raceway; z is the number of single-row rollers; e is the axial distance between the center of the roller coordinate system and the center of the inner ring coordinate system; e.g. of the typerThe distance from the center of the inner ring coordinate system to the center of the system coordinate system; grIs a radial play.
3) Solving the basic rated service life and the corrected service life of the double-row tapered roller bearing according to the load distribution of the bearing raceway, slicing the bearing raceway by adopting a slicing method in the solving process, respectively solving the service life of each slice, and then integrating to obtain the service life of the whole bearing; wherein, the bearing load distribution condition is obtained according to the statics equilibrium equation, the service life of the raceway can be solved, which is as follows:
dividing a bearing raceway into n equal parts, wherein the service life of each section is as follows:
Figure GDA0003292529820000196
Figure GDA0003292529820000197
in the formula: qCihtThe basic rated load of the roller way in the t slice; qCehtThe basic rated load of the roller way in the t slice; qEihtThe equivalent load of the inner raceway of the t-th slice; qEehtThe equivalent load of the t slice outer raceway is shown;
the basic nominal load of each slice is:
Figure GDA0003292529820000201
Figure GDA0003292529820000202
in the formula: bm551.2 is taken as a double-row tapered roller bearing for a rated life correction coefficient; lambda [ alpha ]sCorrection coefficients introduced for correcting the roller edge load and stress concentration (0.61 for the end slices and 1 for the middle slices); Δ l is the length of each slice; dtRoll diameter for the t slice; dpwThe diameter of the pitch circle of the roller group; gamma is a bearing contact angle; gamma ray*Is the structural coefficient of the bearing;
the equivalent load per section of the raceway of the inner ring, i.e. the rotating ring, is:
Figure GDA0003292529820000203
the equivalent load per section of the raceway of the outer ring, i.e. the stationary ferrule, is:
Figure GDA0003292529820000204
the service life of the inner ring and the outer ring of the single-row bearing is as follows:
Figure GDA0003292529820000205
Figure GDA0003292529820000206
the comprehensive service life of the inner ring and the outer ring of the single-row bearing is as follows:
L10m＝L10im+L10em (50)
the basic rated life of the whole bearing is as follows:
Figure GDA0003292529820000211
the whole bearing correction service life is as follows:
La10DRTRB＝a1aisoL10DRTRB (52)
in the above formula: psi is the roller azimuth angle, qihThe contact load is the unit length of the inner ring; q. q.sehThe contact load is the unit length of the outer ring; a is1Is a reliability coefficient; a isisoIs the lube oil coefficient.
The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that the changes in the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims (3)

1. The load distribution and service life calculation method for the double-row tapered roller bearing of the wind generating set is characterized by comprising the following steps of: the method mainly simulates the deformation of an inner ring and a rolling body of the double-row tapered roller bearing based on a coordinate vector, particularly reflects the contact deformation of a raceway and a roller and the contact deformation of the roller and a flange through coordinate transformation, considers the influence of flange deformation, bearing play and roller modification, obtains the load distribution of the bearing raceway by establishing a hydrostatic equilibrium equation of the raceway and the roller, and then solves the service life of the bearing on the basis; which comprises the following steps:
1) the method comprises the following steps of simulating position vectors of a roller and a raceway, and a roller and a flange of a bearing before and after deformation through coordinate vectors, and then converting contact point vector coordinates from a roller coordinate system and an inner ring coordinate system to a system coordinate system through coordinate conversion to establish a deformation coordination equation, wherein the method comprises the following specific steps:
1.1) establishing a system coordinate system Oxyz by taking the center of the bearing as an origin, and establishing an inner ring coordinate system O by taking the center of the inner ring as the originhxhyhzhEstablishing a roller coordinate system O with the roller center as the originwhxwhywhzwhH represents the column;
1.2) determining the amount of deformation
1.2.1) inner ring deformation
Under the coordinate system of the inner ring, the displacement vector of the inner ring under the action of an external load is as follows:
δh＝{δhx,δhy,δhz}T (1)
the vector of the deflection angle of the inner ring is as follows:
γh＝{0,γhy,γhz}T (2)
the coordinates of the center of the inner ring in 3 directions after considering the bearing play are as follows:
Figure FDA0003292529810000011
Figure FDA0003292529810000012
Figure FDA0003292529810000021
in the formula: deltahx，δhy，δhzRespectively, the displacement of the center of the inner ring coordinate system when the play is not considered; gamma rayhy,γhzRespectively as the center of the inner ringh，zhThe angle of deflection of the shaft; delta 'of'hx，δ′hy，δ′hzThe displacement of the center of the inner ring coordinate system when the radial play is considered; e.g. of the typerThe distance from the center of the inner ring coordinate system to the center of the system coordinate system; grIs a radial play; when h is equal to 1, the reaction is carried out,
Figure FDA0003292529810000022
when h is 2, taking the positive value and taking the negative value as the positive value,
Figure FDA0003292529810000023
taking-;
1.2.2) roller deformation
In the roller coordinate system, the displacement vector of the roller is as follows:
Uwh＝{uwhx,0,uwhz}T (6)
the roller rotation angle vector is:
Figure FDA0003292529810000024
in the formula: u. ofwhx，uwhzRespectively, the roller is at xwh，zwhDisplacement of direction;
Figure FDA0003292529810000025
for rolling of rollerswhThe angle of rotation of the direction;
1.3) determining the position of the contact point before deformation
1.3.1) inner circle coordinate System
Z is the contact point of the inner and outer ring raceways and the rollers under the roller coordinate systemwhThe coordinates in the axial direction are:
Figure FDA0003292529810000026
Figure FDA0003292529810000027
Figure FDA0003292529810000028
Figure FDA0003292529810000029
in the formula: dpwIs a pitch circle of a roller groupA diameter; x is the number ofwhi，xwheX is the contact point of the inner raceway and the outer raceway of the ferrule and the roller respectively under the roller coordinate systemwhCoordinates of the axis; epsilon is the roller half-cone angle; alpha and beta are respectively half cone angles of an outer raceway and an inner raceway; γ is the bearing contact angle, c is the normal clearance, when h is 1, c is-1, when h is 2, c is 1; l is the roller length;
the position vectors of the contact points of the inner raceway, the outer raceway and the roller under the inner ring coordinate system are as follows:
Figure FDA0003292529810000031
Figure FDA0003292529810000032
in the formula: e is the axial distance between the center of the roller coordinate system and the center of the inner ring coordinate system; r ishix,rhiy,rhizThe coordinates of the contact point of the roller and the inner raceway under an inner ring coordinate system; r ishex,rhey,rhezThe coordinates of the contact point of the roller and the outer raceway in 3 directions under an inner ring coordinate system are obtained; psi is the azimuth angle of the roller, the roller corresponding to the negative direction of the z-axis in the system coordinate system is the 1 st roller, the azimuth angle is 0, and the azimuth angle of the jth roller is
Figure FDA0003292529810000033
Z is the number of single-row rollers;
the end part of the roller adopts a spherical base surface, and the position vector of the contact point of the roller and the flange under the inner ring coordinate system is as follows:
Figure FDA0003292529810000034
in the formula: r ishfx,rhfy,rhfzThe coordinates of the contact point of the roller and the flange in 3 directions under the inner ring coordinate system are obtained; rsIs the radius of the spherical base surface; theta is an inner ringThe connecting line of the flange and the center of the bearing forms an included angle with the x direction; dwThe diameter of the large end of the roller is adopted, and lambda is a half angle corresponding to the base surface of the ball of the roller;
1.3.2) roller coordinate System
The position vector of the contact point of the roller and the inner and outer raceways under the roller coordinate system is as follows:
Figure FDA0003292529810000041
Figure FDA0003292529810000042
the position vector of the contact point of the roller and the flange under the roller coordinate system is as follows:
Figure FDA0003292529810000043
in the formula: swhfx，swhfy，swhfzCoordinates of the contact point of the roller and the flange in 3 directions under a roller coordinate system are obtained;
1.4) determining the position of the contact point after deformation
1.4.1) inner circle coordinate System
After the inner ring is deformed in a contact manner, the position vector of the contact point of the inner ring raceway and the roller under the inner ring coordinate system is as follows:
Figure FDA0003292529810000044
in the formula:
Figure FDA0003292529810000045
coordinates of the contact point of the inner ring raceway and the roller in 3 directions under an inner ring coordinate system; when h is equal to 1, the reaction is carried out,
Figure FDA0003292529810000046
when h is 2, taking the positive value and taking the negative value as the positive value,
Figure FDA0003292529810000047
taking-;
because the outer raceway is fixed, the position vector of the contact point of the outer raceway and the roller on the inner ring coordinate system is consistent with that before deformation, namely
Figure FDA0003292529810000051
The position vector of the contact point of the roller and the flange under the inner ring coordinate system is as follows:
Figure FDA0003292529810000052
in the formula:
Figure FDA0003292529810000053
the coordinates of the position vector of the contact point of the roller and the flange in 3 directions under the inner ring coordinate system are obtained;
1.4.2) roller coordinate System
The position vector of the contact point of the roller and the inner and outer raceways under the roller coordinate system after the roller is deformed is as follows:
Figure FDA0003292529810000054
Figure FDA0003292529810000055
the position vector of the contact point of the roller and the flange under the roller coordinate system is as follows:
Figure FDA0003292529810000056
1.5) deformation coordination equation
Converting the contact point from the roller coordinate system and the inner ring coordinate system to the system coordinate system through coordinate conversion, then
Figure FDA0003292529810000061
Figure FDA0003292529810000062
Figure FDA0003292529810000063
Figure FDA0003292529810000064
ew＝e+er
Figure FDA0003292529810000065
In the formula: e.g. of the typewIs the distance from the center of the roller coordinate system to the center of the system coordinate system, when h is 1
Figure FDA0003292529810000066
Taken + and taken when h is 2
Figure FDA0003292529810000067
Taking-;
the normal contact deformation of the roller, the inner raceway, the outer raceway and the flange is as follows:
Figure FDA0003292529810000068
Figure FDA0003292529810000069
Figure FDA00032925298100000610
Figure FDA00032925298100000611
Figure FDA00032925298100000612
Figure FDA00032925298100000613
in the formula:
Figure FDA00032925298100000614
respectively are unit normal vectors of the inner ring, the outer ring and the flange; when h is 1
Figure FDA00032925298100000615
Taken + and taken when h is 2
Figure FDA00032925298100000616
Taking-;
2) establishing a roller static equilibrium equation and a bearing outer ring static equilibrium equation according to a deformation coordination equation, and performing iterative solution on accurate load distribution of a raceway and a flange according to a Newton-Raphson equation;
3) the basic rated service life and the corrected service life of the double-row tapered roller bearing are solved according to the load distribution of the bearing raceway, the bearing raceway is sliced by adopting a slicing method in the solving process, the service life of each slice is respectively solved, and then the service life of the whole bearing is obtained through integration.
2. The method for calculating the load distribution and the service life of the double-row tapered roller bearing of the wind generating set according to claim 1, wherein the method comprises the following steps: in step 2), the details of the roller static balance equation are as follows:
and (3) carrying out stress analysis on a single roller, wherein the balance equation is as follows:
Qi+Qe+Fc＝0 (28)
Ti+Te+Mg＝0 (29)
Figure FDA0003292529810000071
Figure FDA0003292529810000072
Figure FDA0003292529810000073
Figure FDA0003292529810000074
Figure FDA0003292529810000075
Mg＝JrωGωZsinγ (35)
in the formula: ki,KeThe contact stiffness of the inner ring and the outer ring is respectively; qi，QeRespectively the contact part load of the roller and the inner ring and the contact part load of the outer ring; t isi，TeThe moment acted on the roller by the inner and outer ring raceways respectively; fcIs rolledThe centrifugal force of the seed; mgA gyroscopic moment that is a roller; m is the mass of a single tapered roller; rGThe radius of rotation of the roller centroid; omegaGIs the revolution angular velocity of the roller; j. the design is a squarerIs the roller moment of inertia; omegaZIs the roller rotation angular velocity; deltahi(xwhiψ) is the normal contact deformation of the roller with the inner raceway, δhe(xwhePsi) is the normal contact deformation of the roller and the outer raceway; x is the number ofwhi，xwheX is the contact point of the inner raceway and the outer raceway of the ferrule and the roller respectively under the roller coordinate systemwhCoordinates of the axis; psi is the roller azimuth; gamma is the contact angle of the bearing;
the outer ring static equilibrium equation has the following specific conditions:
and (3) carrying out stress analysis on the outer ring, wherein the balance equation is as follows:
Figure FDA0003292529810000081
Figure FDA0003292529810000082
Figure FDA0003292529810000083
Figure FDA0003292529810000084
Figure FDA0003292529810000085
Figure FDA0003292529810000086
Figure FDA0003292529810000087
in the formula: fx，Fy，Fz，My，MzThe loads in five directions at the center of the bearing; q. q.sheThe contact load is the contact load of the outer ring and the roller contact point position in unit length; when h is 1
Figure FDA0003292529810000088
Taken + and taken when h is 2
Figure FDA0003292529810000089
Taking-;
the statics equilibrium equation solving process is as follows:
solving according to the established roller static balance equation and the outer ring static balance equation, wherein the solving process comprises the following steps: 1) inputting main structural parameters of a bearing: l, Rs，Dw，θ，α，β，Z，e，er，Gr(ii) a 2) Inputting working condition parameters: fx，Fy，Fz，My，Mz(ii) a 3) Giving a roller deformation initial value and an inner ring deformation initial value; 4) performing iterative calculation through formulas (28) to (42) to obtain raceway load distribution;
wherein l is the roller length; rsIs the radius of the spherical base surface; dwThe diameter of the big end of the roller; theta is an included angle between a connecting line of the inner ring flange and the center of the bearing and the x direction; alpha and beta are respectively half cone angles of an outer raceway and an inner raceway; z is the number of single-row rollers; e is the axial distance between the center of the roller coordinate system and the center of the inner ring coordinate system; e.g. of the typerThe distance from the center of the inner ring coordinate system to the center of the system coordinate system; grIs a radial play.
3. The method for calculating the load distribution and the service life of the double-row tapered roller bearing of the wind generating set according to claim 1, wherein the method comprises the following steps: in the step 3), the bearing load distribution condition is obtained according to the statics equilibrium equation, and then the service life of the raceway can be solved, specifically as follows:
dividing a bearing raceway into n equal parts, wherein the service life of each section is as follows:
Figure FDA0003292529810000091
Figure FDA0003292529810000092
in the formula: qCihtThe basic rated load of the roller way in the t slice; qCehtThe basic rated load of the roller way in the t slice; qEihtThe equivalent load of the inner raceway of the t-th slice; qEehtThe equivalent load of the t slice outer raceway is shown;
the basic nominal load of each slice is:
Figure FDA0003292529810000093
Figure FDA0003292529810000094
in the formula: bmA rated life correction factor; lambda [ alpha ]sCorrection coefficients introduced to correct edge loading and stress concentrations of the roller; Δ l is the length of each slice; dtRoll diameter for the t slice; dpwThe diameter of the pitch circle of the roller group; gamma is a bearing contact angle; gamma ray*Is the structural coefficient of the bearing;
the equivalent load per section of the raceway of the inner ring, i.e. the rotating ring, is:
Figure FDA0003292529810000095
the equivalent load per section of the raceway of the outer ring, i.e. the stationary ferrule, is:
Figure FDA0003292529810000101
the service life of the inner ring and the outer ring of the single-row bearing is as follows:
Figure FDA0003292529810000102
Figure FDA0003292529810000103
the comprehensive service life of the inner ring and the outer ring of the single-row bearing is as follows:
L10m＝L10im+L10em (50)
the basic rated life of the whole bearing is as follows:
Figure FDA0003292529810000104
the whole bearing correction service life is as follows:
La10DRTRB＝a1aisoL10DRTRB (52)
in the above formula: psi is the roller azimuth angle, qihThe contact load is the unit length of the inner ring; q. q.sehThe contact load is the unit length of the outer ring; a is1Is a reliability coefficient; a isisoIs the lube oil coefficient.
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